This invention relates to a method and apparatus for controlling the roll gap of a cold rolling mill designed to roll steel sheets or sheets of nonferrous metals, such as aluminum, to obtain products having definite thickness.
In order to set the roll gap of a rolling mill to a desired value, it is necessary to measure or estimate the rolling pressure. Generally, however, the rolling pressure is not distributed uniformly along the contact arc between the working rolls of the mill and the strip being rolled due to variations in the coefficient of friction between the working rolls and the strip and variations in the deformation resistance of the strip. Accordingly, it is necessary to precisely calculate the distribution of the rolling pressure in order to correctly determine the rolling pressure. The use of such calculation as a model for controlling a cold mill with an electronic computer complicates the calculation and hence is not practical. Accordingly, it has been the general practice to predetermine the rolling pressure by using the following equation 1 which is usually used to obtain the rolling pressure of a cold mill in which the coefficient of friction and the deformation resistance are expressed as mean definite values. EQU p = Z . Km.sqroot.R'. .DELTA.h . Qp 1
Where
p : the rolling load per unit width in kg/mm, PA1 Z : the compensation coefficient for tension, PA1 KM : the mean deformation resistance in kg/mm.sup.2, PA1 R' : the roll radius in mm after the roll has been slightly flattened by contact with the material being rolled, PA1 .DELTA. h : the amount of reduction mm, and PA1 Qp : the function regarding the rolling force. PA1 Kf : the deformation resistance in kg/mm.sup.2, PA1 r : the mean total reduction, PA1 r.sub.E : the total reduction of the strip on the entrance side, PA1 r.sub.x : the total reduction of the strip on the exit side, PA1 .beta..sub.1 : the distribution coefficient of the reduction (to be described later in detail in connection with the distribution coefficient of temperature)
Although it is necessary to determine the mean deformation resistance Km, in the case of cold rolling, the resistance is different at the entrance and the exit sides of the mill due to the hardening of the material caused by rolling. For this reason, it is usual to calculate the mean total reduction r which is used to determine the mean deformation resistance Km from the overall reduction rate of the material at the entrance and exit sides on the assumption that the deformation resistance of the material is a function of the total reduction (the reduction at an instant after the strain becomes zero). The values of Km and r at this time are expressed by the following equations 2 and 3. EQU Km = 1.15 Kf (r) 2 EQU r = .beta..sub.1 r.sub.E + (1 - .beta..sub.1)r.sub.x 3
where
However, the strain rate of the strip during rolling varies depending upon the rolling conditions. Further, the deformation resistance decreases due to the heat generated by plastic deformation of the material. In modern cold mills operating at high rolling speeds, it is impossible to ignore the effects of the strain rate and the strip temperature upon the deformation resistance of the material.
Accordingly, in order to improve the quality of the product it is important to accurately determine the deformation resistance of the material whereby to more accurately control the setting of the roll gap. To this end, the deformation resistance should be determined as a function of the total reduction, the strain rate and the strip temperature.
When determining the mean deformation resistance on the assumption that the deformation resistance is a function of the total reduction, the strain rate and the strip temperature, how to determine the mean total reduction or the strip temperature presents a problem.
As above described, the coefficient of friction between the rolls of a cold rolling mill and the material and the deformation resistance thereof are unknown factors involved in the mathematical model for setting the roll gap of the mill, so that the accuracy and the complexity of the mathematical model are determined by the manner of handling these two factors.
Although it is possible to determine relatively easily the deformation resistance of the material in a factory or laboratory by using a tension testing machine or the like, the coefficient of friction must be determined by using a commercial rolling mill to which the invention is to be applied and where there is a number of types of the material, such as aluminum, it is not only difficult to determine at high accuracies the coefficient of friction for all types of the material but this also requires much time. For this reason, it is possible to more readily form the model and to simplify the form thereof by determining a correct value of the deformation resistance for each material and to make simpler the form of the model.
Since the recrystallization temperature of aluminum is low, it is not permissible to ignore the effect of lowering the deformation resistance caused by the temperature rise due to rolling. Rolling oil is often used to make flat and smooth the surface of the rolled product so that it is necessary to use oil having a low boiling point and hence it vaporizes at a relatively low temperature. For this reason, when the temperature of the material increases due to the rolling operation there is a danger of a fire hazard. Accordingly, it is necessary to determine the extent of temperature rise of the material caused by rolling for the purpose of reflecting it upon the deformation resistance.